Te Tāpiri Wāhanga o ngā Wekita
I roto i te pāngarau me te ahupūngao, he ariā taketake ngā whārite. Ka whakamahia ēnei hei whakaahua i ngā rahinga he ahunga, he rahi hoki. He mea nui te mōhio ki te tāpiri whārite i roto i te whānuitanga o ngā tono pūtaiao me ngā tono hangarau. Ko tētahi o ngā tikanga tino noa mō te tāpiri whārite ko te tāpiri wāhanga. Ka whakamāramahia e tēnei tuhinga ngā mātāpono taketake o te tāpiri whārite, te ariā o ngā wāhanga whārite, me ngā mahi mō te tāpiri whārite wāhanga.
He aha te Wetere?
I mua i te ruku hohonu ki te tāpiritanga whārite, me mārama tātou he aha te whārite. Ko te whārite he mea pāngarau me ngā āhuatanga matua e rua: te rahi (te roa rānei) me te ahunga. Ko tētahi tauira māmā o te whārite i roto i te oranga o ia rā ko te nekehanga o tētahi mea. Hei tauira, ki te hikoi tetahi i te 5 kiromita ki te raki, ka taea e tātou te whakaatu i taua haerenga me tētahi whārite he 5 kiromita te rahi me te ahunga ki te raki.
He maha ngā wā ka whakaaturia ngā whārite mā te whakairoiro hei pere, ko te roa o te pere e tohu ana i te rahi, ā, ko te ahunga o te pere e tohu ana i te whārite. Ka taea hoki te whakaatu i ngā whārite hei wāhanga e whakarara ana ki ngā tuaka taunga, pērā i ngā tuaka x, y, me z i roto i tētahi pūnaha taunga toru-ahu.
Ngā Wāhanga Wetereo
Ka taea te wehewehe i tētahi whārite i roto i ngā āhuatanga e rua, e toru rānei, kia rite ki ngā wāhanga e whakarara ana ki ngā tuaka taunga. Hei tauira, ka taea te wehewehe i tētahi whārite rua-āhua me te uara (3, 4) me te wāhanga x = 3 me te wāhanga y = 4. I roto i ngā kupu āhuahanga, ko te tikanga o tēnei ka taea te tiro i te whārite hei te tapeke o ngā whārite e rua: tētahi whārite e whakarara ana ki te tuaka-x me te rahi 3, me tētahi whārite e whakarara ana ki te tuaka-y me te rahi 4.
Mō tētahi whārite toru-ahu, e toru ā tātou wāhanga: x, y, me z. Hei tauira, ko ngā wāhanga o te whārite (3, 4, 5) ko x = 3, y = 4, me z = 5. I roto i tētahi pūnaha taunga Cartesian, ka taea te whakaatu i tēnei whārite hei pere e tīmata ana mai i te pūtake (0, 0, 0) ka mutu ki te pūwāhi (3, 4, 5).
Te Tāpiri Wāhanga o ngā Wekita
Nā, ka matapakihia e tātou te tāpiri i ngā whārite mā te whakamahi i te tikanga componentwise. Ko te tāpiri whārite componentwise ko te tāpiri i ia wāhanga motuhake. He tikanga tino whai hua, he tikanga whai hua hoki tēnei, inā koa ka mahi tahi me ngā whārite i roto i te pūnaha taunga Cartesian.
Ngā Hipanga mō te Tāpiri Wāhanga o ngā Wekita
1. Wehea te whārite ki ōna wāhanga:
Hei taahiraa tuatahi, me wehewehe e tātou ia irahiko hei tāpiri atu ki roto i ōna wāhanga e whakarara ana ki ngā tuaka x, y, me z (mēnā he tuaka).
2. Te tāpiri i ngā wāhanga whakarara:
Mō ia tuaka (x, y, me z), ka tāpirihia e tātou ngā wāhanga whakarara. Hei tauira, ko te wāhanga-x o te tapeke ko te tapeke o ngā wāhanga-x katoa o ngā whārite e tāpirihia ana.
3. Whakakotahitia anō ngā wāhanga kua tāpirihia:
Kia tāpirihia ngā wāhanga katoa, ka honoa anōtia ngā wāhanga kia puta ai te tapeke o te wetere.
Me titiro tātou ki tētahi tauira tuturu hei whakamārama ake i tēnei ariā.
Tauira o te Tāpiritanga Wekita i ngā Ahu e Rua
Me kī he rua ā tātou pūwero i roto i ngā āhuahanga e rua:
– Te Wētera A = (3, 4)
– Te Wēra B = (1, 2)
Hipanga 1: Wehewehea ia pūwhakaahua ki ōna wāhanga:
– A_x = 3, A_y = 4
– B_x = 1, B_y = 2
Hipanga 2: Tāpirihia ngā wāhanga whakarara:
– Te hua o te wāhanga x: A_x + B_x = 3 + 1 = 4
– Te hua o te wāhanga y: A_y + B_y = 4 + 2 = 6
Hipanga 3: Whakakotahitia ngā wāhanga kua tāpirihia:
– Te hua whārite = (4, 6)
Nō reira, ko te hua o te tāpiri i ngā whārite A me B ko te whārite (4, 6).
Tauira o te Tāpiritanga Wekita i roto i ngā Ahu-Toru
Ka taea hoki e tātou te whakawhānui i tēnei tauira ki ngā ahu-toru. Me kī he rua ā tātou whārite i roto i ngā ahu-toru:
– Te Wēra C = (2, -1, 3)
– Te Wētera D = (1, 4, -2)
Hipanga 1: Wehewehea ia pūwhakaahua ki ōna wāhanga:
– C_x = 2, C_y = -1, C_z = 3
– D_x = 1, D_y = 4, D_z = -2
Hipanga 2: Tāpirihia ngā wāhanga whakarara:
– Hua o te wāhanga x: C_x + D_x = 2 + 1 = 3
– Te hua o te wāhanga y: C_y + D_y = -1 + 4 = 3
– Te hua o te wāhanga z: C_z + D_z = 3 – 2 = 1
Hipanga 3: Whakakotahitia ngā wāhanga kua tāpirihia:
– Te hua whārite = (3, 3, 1)
Ko te hua o te tāpiri i ngā whārite C me D ko te whārite (3, 3, 1).
Te Hiranga o te Tāpiritanga Wekita i te Oranga o Ia Rā
Ahakoa te āhua o te tāpiritanga whārite ā-wāhanga he kaupapa ngaro, he tono mahi tōna i roto i te oranga o ia rā me ngā mara hangarau. Ko ētahi tauira tono ko:
1. Ahupūngao: He maha ngā ariā o te ahupūngao, pērā i te kaha, te whakaterenga, me te tere, e whakaatuhia ana hei whārite. He maha ngā wā ka whakamahia te tāpiri whārite hei tatau i te kaha, te tere rānei ka puta mai.
2. Hangarau: I roto i te hangarau, ka whakamahia ngā whārite mō te tātari hanganga, te hihiri wai, me te hikohiko. Mā te tāpiri wāhanga o ngā whārite ka āwhina i ngā kaihangarau ki te hoahoa me te tātari i ngā pūnaha uaua.
3. Whakairoiro Rorohiko: Ka whakamahia ngā weketara i roto i ngā whakairoiro rorohiko hei whakaahua i te tūranga, te tere, me te whakaterenga o ngā mea. He mea nui te tāpiri weketara i ia wāhanga i roto i te whanaketanga o te pakiwaituhi me te whakatauira.
4. Whakatere: I roto i te whakatere, ahakoa mā te whenua, mā te moana, mā te rangi rānei, ka whakamahia te tāpiritanga whārite hei whakatau i te ara me te tūnga. Hei tauira, ka whakamahia e te hangarau GPS ngā mātāpono whārite hei tatau i te ara tino whai hua.
Mā te mārama ki ngā ariā taketake me ngā tono mahi o te tāpiritanga whārite ā-wāhanga, ka taea e tātou te mārama ki te hiranga o ngā whārite i roto i ngā āhuatanga maha o te ao hou me te hangarau.
Whakamutunga
He tikanga whai hua, he tikanga whai hua hoki te tāpiri i ngā whārite wāhanga hei tāpiri i ngā whārite ki roto i tētahi pūnaha taunga Cartesian. Mā te wehewehe i tētahi whārite ki ōna wāhanga e whakarara ana ki ngā tuaka taunga, ka taea e tātou te tāpiri i aua wāhanga motuhake i mua i te whakakotahi i a rātou kia whiwhi ai i te whārite hua. He maha ngā tono mahi a tēnei tikanga i roto i te ahupūngao, te hangarau, te whakairoiro rorohiko, te whakatere, me ētahi atu. Ko te mārama ki te tāpiri i ngā whārite wāhanga ehara i te mea ka whakapakari noa i ō tātou turanga pāngarau me te ā-tinana engari ka whakatuwhera hoki i te kuaha ki te whānuitanga o ngā tono hangarau me te pūtaiao matatau.
